On some properties of the undetected error probability of linear codes (Corresp.)

A recent paper [1] discussed the
2^{-p}
bound (where
p = n- k
) for the probability of undetected error
P(\epsilon)
for an
(n,k)
block code used for error detection on a binary symmetric channel. This investigation is continued and extended and dual codes are studied. The dual and extension of a perfect code obey the
2^{-p}
bound, but this is not necessarily true for arbitrary codes that obey the bound. Double-error-correcting BCH codes are shown to obey the bound. Finally the problem of constructing uniformly good codes is examined.